Consult with a local real etate attorney. However, you may want to consider what will happen to your property if you are deported? If you do intend to hold title, you should have a power of attorney in place with someone who does have legal status in the United States, to step in and have the ability to undertake financial transactions related to the property; if you were to be deported.
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With a cash payment, you should be able to buy and hold the property in your own name. Work with a local real estate attorney, I do not believe your immigration status will even factor into this.
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I agree with my colleague that you should contact a real estate attorney. Immigration status should not be a factor in an all cash purchase.
Samuel Ouya Maina, Esq. 415.391.6612 email@example.com Law Offices of S. Ouya Maina, PC 332 Pine Street, Suite 707 San Francisco, CA 94104